Finite Group Databasebeta

← C151×#24655 #50329580

Subgroups — C151×#24655 #50329580

Order 38656.

922 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#464×C151C211yesmaximal, characteristic, complemented
2C2×#431×C151C211yesmaximal, characteristic, complemented
3#2850×C151C211yesmaximal, characteristic
4C4×C22⋊Q8×C151C211yesmaximal, characteristic, complemented
5#2035×C151C211yesmaximal, characteristic, complemented
6#2033×C151C211yesmaximal, characteristic
7#2001×C151C211yesmaximal, characteristic, complemented
8#2000×C151C211yesmaximal, characteristic
9#1983×C151C211yesmaximal, characteristic, complemented
10#1969×C151C211yesmaximal, characteristic, complemented
11#1968×C151C211yesmaximal, characteristic, complemented
12#1949×C151C211yesmaximal, characteristic, complemented
13#1934×C151C211yesmaximal, characteristic, complemented
14#1933×C151C211yesmaximal, characteristic, complemented
15#1805×C151C211yesmaximal, characteristic, complemented
16C22×Q16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C2×#124×C151C2211yescharacteristic
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×#121×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C22×C42×C151C2211yescharacteristic
24#464×C151—24no—
25#431×C151—24no—
26C2×#107×C151C2211yescharacteristic
27C2×#106×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#103×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×C4×C8×C151C2211yescharacteristic
41C2×C4×C8×C151C2211yescharacteristic
42#391×C151C2211yescharacteristic
43#391×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#389×C151C2211yescharacteristic
46#388×C151—21no—
47#388×C151—21no—
48#387×C151—21no—
49#386×C151—21no—
50#386×C151—21no—
51#385×C151—21no—
52#382×C151C2211yescharacteristic
53#380×C151C2211yescharacteristic
54C4×C4⋊C4×C151—21no—
55C4×C4⋊C4×C151C2211yescharacteristic
56C4×C22⋊C4×C151—21no—
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×Q8×C151C2311yescharacteristic
63C22×D4×C151—21no—
64C22×D4×C151C2311yescharacteristic
65C23×C4×C151D411yescharacteristic
66C23×C4×C151D411yescharacteristic
67C23×C4×C151C2311yescharacteristic
68C2×Q16×C151—22no—
69C2×Q16×C151—22no—
70C2×Q16×C151—41no—
71C2×SD16×C151—22no—
72C2×SD16×C151—22no—
73C2×SD16×C151—41no—
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78#124×C151—22no—
79#124×C151—22no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—41no—
83C22⋊Q8×C151—41no—
84#121×C151—41no—
85#121×C151—41no—
86C4×Q8×C151—22no—
87C4×Q8×C151—22no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151C2311yescharacteristic
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C22⋊C4×C151—21no—
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C42×C151—22no—
106C2×C42×C151—22no—
107C2×C42×C151—21no—
108C2×C42×C151—21no—
109C2×C42×C151D411yescharacteristic
110C2×C42×C151D411yescharacteristic
111C2×C42×C151C2311yescharacteristic
112C2×C42×C151C2311yescharacteristic
113#107×C151—41no—
114#106×C151—41no—
115C4⋊C8×C151—22no—
116C4⋊C8×C151D414yescomplemented
117#103×C151—22no—
118#103×C151—22no—
119#103×C151—41no—
120#103×C151—41no—
121#103×C151—41no—
122#102×C151—22no—
123#102×C151—22no—
124#102×C151—41no—
125C22⋊C8×C151—22no—
126C22⋊C8×C151—22no—
127C4×C8×C151—22no—
128C4×C8×C151—22no—
129#95×C151—21no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138C24×C151—21no—
139C24×C151C2×D411yescharacteristic
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151#4112yes—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—42no—
159C2×D4×C151—42no—
160C2×D4×C151—42no—
161C22×C4×C151—22no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—41no—
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2411yescharacteristic
186Q16×C151—44no—
187SD16×C151—44no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151C2×D412yes—
199C2×C8×C151C2×D412yes—
200C4⋊C4×C151—24no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—42no—
211C4⋊C4×C151—42no—
212C4⋊C4×C151—42no—
213C4⋊C4×C151#4112yes—
214C22⋊C4×C151—24no—
215C22⋊C4×C151—42no—
216C22⋊C4×C151—42no—
217C22⋊C4×C151—42no—
218C22⋊C4×C151—42no—
219C22⋊C4×C151—42no—
220C22⋊C4×C151—42no—
221C22⋊C4×C151—42no—
222C42×C151—22no—
223C42×C151—22no—
224C42×C151—21no—
225C42×C151—21no—
226C42×C151—42no—
227C42×C151—42no—
228C42×C151C2×D412yes—
229C42×C151#4112yes—
230C23×C151—21no—
231C23×C151—21no—
232C23×C151—21no—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—41no—
237C23×C151—41no—
238C23×C151—41no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151#13512yes—
244C23×C151C22×D411yescharacteristic
245Q8×C151—22no—
246Q8×C151—22no—
247Q8×C151—41no—
248Q8×C151—41no—
249Q8×C151—41no—
250Q8×C151—41no—
251Q8×C151—41no—
252Q8×C151—41no—
253D4×C151—41no—
254D4×C151—41no—
255D4×C151—41no—
256D4×C151—41no—
257D4×C151—84no—
258C2×C4×C151—28no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—22no—
269C2×C4×C151—22no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—44no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151#12112yes—
297C2×C4×C151#12112yes—
298C2×C4×C151#13512yes—
299C2×C4×C151#13712yes—
300C2×C4×C151C22×D411yescharacteristic
301C2×C4×C151C2×#4111yescharacteristic
302C2×C4×C151C2×#4111yescharacteristic
303C2×C4×C151C2×#4111yescharacteristic
304C2×C4×C151H(5,𝔽2)11yescharacteristic
305C2×C4×C151H(5,𝔽2)11yescharacteristic
306C8×C151—22no—
307C8×C151—22no—
308C8×C151—41no—
309C8×C151—41no—
310C22×C151—22no—
311C22×C151—22no—
312C22×C151—22no—
313C22×C151—41no—
314C22×C151—41no—
315C22×C151—41no—
316C22×C151—41no—
317C22×C151—81no—
318C22×C151—81no—
319C22×C151—81no—
320C22×C151—81no—
321C22×C151—81no—
322C22×C151—81no—
323C22×C151—81no—
324C22×C151C2×#12111yescharacteristic
325C22×C151#52511yescharacteristic
326C22×C151#53511yescharacteristic
327C22×C151C2×#13511yescharacteristic
328C22×C151C2×#13511yescharacteristic
329C22×C151C2×#13711yescharacteristic
330C22×C151#57511yescharacteristic
331C4×C151—22no—
332C4×C151—22no—
333C4×C151—22no—
334C4×C151—22no—
335C4×C151—42no—
336C4×C151—41no—
337C4×C151—42no—
338C4×C151—81no—
339C4×C151—81no—
340C4×C151—81no—
341C4×C151—81no—
342C4×C151—81no—
343C4×C151#54611yescharacteristic
344C4×C151#55011yescharacteristic
345C4×C151#55311yescharacteristic
346C4×C151#55511yescharacteristic
347C2×C151—42no—
348C2×C151—161no—
349C2×C151#241411yescharacteristic
350C2×C151#305011yescharacteristic
351C2×C151#305611yescharacteristic
352C2×C151#310211yescharacteristic
353C2×C151#310811yescharacteristic
354C2×C151#321011yescharacteristic
355C2×C151#321111yescharacteristic
356#24655C15111yesmaximal, characteristic, direct product factor, Sylow
357C151#2465511yescharacteristic, direct product factor, Sylow
358C2×#464C2×C15111yescharacteristic, complemented
359C2×#431C2×C15111yescharacteristic, complemented
360#2850C2×C15111yescharacteristic
361C4×C22⋊Q8C2×C15111yescharacteristic, complemented
362#2035C2×C15111yescharacteristic, complemented
363#2033C2×C15111yescharacteristic
364#2001C2×C15111yescharacteristic, complemented
365#2000C2×C15111yescharacteristic
366#1983C2×C15111yescharacteristic, complemented
367#1969C2×C15111yescharacteristic, complemented
368#1968C2×C15111yescharacteristic, complemented
369#1949C2×C15111yescharacteristic, complemented
370#1934C2×C15111yescharacteristic, complemented
371#1933C2×C15111yescharacteristic, complemented
372#1805C2×C15111yescharacteristic, complemented
373C22×Q16C22×C15111yescharacteristic
374C22×SD16C22×C15111yescharacteristic
375C2×#124C22×C15111yescharacteristic
376C2×C22⋊Q8C22×C15111yescharacteristic
377C2×C22⋊Q8C22×C15111yescharacteristic
378C2×#121C22×C15111yescharacteristic
379C2×C4×Q8C22×C15111yescharacteristic
380C22×C42C22×C15111yescharacteristic
381#464—24no—
382#431—24no—
383C2×#107C22×C15111yescharacteristic
384C2×#106C22×C15111yescharacteristic
385C2×C4⋊C8C22×C15111yescharacteristic
386C2×C4⋊C8C22×C15111yescharacteristic
387C2×#103C22×C15111yescharacteristic
388C2×#103C22×C15111yescharacteristic
389C2×#103C22×C15111yescharacteristic
390C2×#103C22×C15111yescharacteristic
391C2×#103C22×C15111yescharacteristic
392C2×#102C22×C15111yescharacteristic
393C2×#102C22×C15111yescharacteristic
394C2×#102C22×C15111yescharacteristic
395C2×C22⋊C8C22×C15111yescharacteristic
396C2×C22⋊C8C22×C15111yescharacteristic
397C2×C4×C8C22×C15111yescharacteristic
398C2×C4×C8C22×C15111yescharacteristic
399#391C22×C15111yescharacteristic
400#391C22×C15111yescharacteristic
401#390C22×C15111yescharacteristic
402#389C22×C15111yescharacteristic
403#388—21no—
404#388—21no—
405#387—21no—
406#386—21no—
407#386—21no—
408#385—21no—
409#382C22×C15111yescharacteristic
410#380C22×C15111yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4C22×C15111yescharacteristic
413C4×C22⋊C4—21no—
414#340C22×C15111yescharacteristic
415#340C22×C15111yescharacteristic
416#340C22×C15111yescharacteristic
417#340C22×C15111yescharacteristic
418C22×Q8C23×C15111yescharacteristic
419C22×Q8C23×C15111yescharacteristic
420C22×D4—21no—
421C22×D4C23×C15111yescharacteristic
422C23×C4D4×C15111yescharacteristic
423C23×C4D4×C15111yescharacteristic
424C23×C4C23×C15111yescharacteristic
425C2×Q16—22no—
426C2×Q16—22no—
427C2×Q16—41no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—41no—
431C22×C8C23×C15111yescharacteristic
432C22×C8C23×C15111yescharacteristic
433C22×C8C23×C15111yescharacteristic
434C22×C8C23×C15111yescharacteristic
435#124—22no—
436#124—22no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—41no—
440C22⋊Q8—41no—
441#121—41no—
442#121—41no—
443C4×Q8—22no—
444C4×Q8—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4C23×C15111yescharacteristic
450C2×C4⋊C4C23×C15111yescharacteristic
451C2×C4⋊C4C23×C15111yescharacteristic
452C2×C4⋊C4C23×C15111yescharacteristic
453C2×C4⋊C4C23×C15111yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42D4×C15111yescharacteristic
467C2×C42D4×C15111yescharacteristic
468C2×C42C23×C15111yescharacteristic
469C2×C42C23×C15111yescharacteristic
470#107—41no—
471#106—41no—
472C4⋊C8—22no—
473C4⋊C8D4×C15114yescomplemented
474#103—22no—
475#103—22no—
476#103—41no—
477#103—41no—
478#103—41no—
479#102—22no—
480#102—22no—
481#102—41no—
482C22⋊C8—22no—
483C22⋊C8—22no—
484C4×C8—22no—
485C4×C8—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C24—21no—
496C24C2×D4×C15111yescharacteristic
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8#41×C15112yes—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—41no—
537C22×C4C2×D4×C15111yescharacteristic
538C22×C4C2×D4×C15111yescharacteristic
539C22×C4C2×D4×C15111yescharacteristic
540C22×C4C2×D4×C15111yescharacteristic
541C22×C4C2×D4×C15111yescharacteristic
542C22×C4C24×C15111yescharacteristic
543Q16—44no—
544SD16—44no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8C2×D4×C15112yes—
556C2×C8C2×D4×C15112yes—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4#41×C15112yes—
571C22⋊C4—24no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C42—22no—
580C42—22no—
581C42—21no—
582C42—21no—
583C42—42no—
584C42—42no—
585C42C2×D4×C15112yes—
586C42#41×C15112yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23#135×C15112yes—
601C23C22×D4×C15111yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—84no—
615C2×C4—28no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—44no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4#121×C15112yes—
654C2×C4#121×C15112yes—
655C2×C4#135×C15112yes—
656C2×C4#137×C15112yes—
657C2×C4C22×D4×C15111yescharacteristic
658C2×C4C2×#41×C15111yescharacteristic
659C2×C4C2×#41×C15111yescharacteristic
660C2×C4C2×#41×C15111yescharacteristic
661C2×C4H(5,𝔽2)×C15111yescharacteristic
662C2×C4H(5,𝔽2)×C15111yescharacteristic
663C8—22no—
664C8—22no—
665C8—41no—
666C8—41no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#121×C15111yescharacteristic
682C22#525×C15111yescharacteristic
683C22#535×C15111yescharacteristic
684C22C2×#135×C15111yescharacteristic
685C22C2×#135×C15111yescharacteristic
686C22C2×#137×C15111yescharacteristic
687C22#575×C15111yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—41no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4#546×C15111yescharacteristic
701C4#550×C15111yescharacteristic
702C4#553×C15111yescharacteristic
703C4#555×C15111yescharacteristic
704C2—42no—
705C2—161no—
706C2#2414×C15111yescharacteristic
707C2#3050×C15111yescharacteristic
708C2#3056×C15111yescharacteristic
709C2#3102×C15111yescharacteristic
710C2#3108×C15111yescharacteristic
711C2#3210×C15111yescharacteristic
712C2#3211×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#464×C151C2semidirect
2. C2×#431×C151C2semidirect
4. C4×C22⋊Q8×C151C2semidirect
5. #2035×C151C2semidirect
7. #2001×C151C2semidirect
9. #1983×C151C2semidirect
10. #1969×C151C2semidirect
11. #1968×C151C2semidirect
12. #1949×C151C2semidirect
13. #1934×C151C2semidirect
14. #1933×C151C2semidirect
15. #1805×C151C2semidirect
116. C4⋊C8×C151D4semidirect
356. #24655C151direct (N × H)
357. C151#24655direct (N × H)
358. C2×#464C2×C151semidirect
359. C2×#431C2×C151semidirect
361. C4×C22⋊Q8C2×C151semidirect
362. #2035C2×C151semidirect
364. #2001C2×C151semidirect
366. #1983C2×C151semidirect
367. #1969C2×C151semidirect
368. #1968C2×C151semidirect
369. #1949C2×C151semidirect
370. #1934C2×C151semidirect
371. #1933C2×C151semidirect
372. #1805C2×C151semidirect
473. C4⋊C8D4×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#464×C1512
C2×#431×C1512
#2850×C1512
C4×C22⋊Q8×C1512
#2035×C1512
#2033×C1512
#2001×C1512
#2000×C1512
#1983×C1512
#1969×C1512
#1968×C1512
#1949×C1512
#1934×C1512
#1933×C1512
#1805×C1512
#24655151